Public Choice

, Volume 178, Issue 1–2, pp 53–65 | Cite as

The elimination paradox: apportionment in the Democratic Party

  • Michael A. Jones
  • David McCune
  • Jennifer WilsonEmail author


To award delegates in their presidential primary elections, the US Democratic Party uses Hamilton’s method of apportionment after eliminating any candidates (and their votes) that receive less than 15% of the total votes cast. We illustrate how a remaining candidate may have his or her delegate total decline as a result of other candidates being eliminated; this leads to a new elimination paradox. We relate that paradox to the new states, no show, and population paradoxes and show that divisor methods are not susceptible to the elimination paradox. We conclude with instances in which the elimination paradox may occur in other contexts, including parliamentary systems.


Elimination paradox Democratic primary Population monotonicity 

Mathematics Subject Classification

91B32 91B12 91F10 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical ReviewsAnn ArborUSA
  2. 2.William Jewell CollegeLibertyUSA
  3. 3.Eugene Lang College, The New SchoolNew York CityUSA

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